The most powerful navies in the world. You may disagree but this is my top 10.

1. US Navy. The most powerful without a doubt.
2. Russian Navy. Still has a lot of big ships and nuclear subs.
3. Japanese Navy. No aircraft carriers but many modern destroyers with AEGIS system and US technology.
4. French Navy. Modern navy with a Nuclear carrier and submarines.
5. Royal Navy. The Invencibles are old and limited but the British always count.
6. Chinese Navy. Lots of destroyers but many of them old and obsolete.
7. Italian Navy. A considerable navy with carrier projecion power
8. Spanish Navy. Similar to Italian navy. AEGIS destroyers.
9. South Korea Navy. Modern ships and amphibious capability. AEGIS technology.
10. Indian Navy. Considerable number of ships. Old aircraft carrier (ex-HMS Hermes).

I would drop the Japanese Navy several slots, as they have no ballistic missile submarines nor do they have any aircraft carriers. The JMSDF's new Hyuga, while having fixed wing capability, does not have an organic air group.

Major moves in the next decade.
Royal Navy - Betting heavily that the HMS Queen Elizabeth carriers will be a success. But, will they matter. Great Britain has been paying off escort ships left & right, meanwhile only six Type 45s are to be constructed as replacements. Overall, it looks like the Queen will be quite vulnerable to attack with her limited number of escorts.

Russian Navy - Will either retain its slot or slip a notch or two. Many old ships, but the promise of new ships and increased funding means the Russian navy will be one to watch.

Chinese Navy - A lot of modernization going on here. It can only improve its position.

Indian Navy - Another rising star. The next decade looks promising for the Indian navy.

We could drop the Russian and Japanese navies a couple of slots but I still consider them superior to the Chinese. The French and British take second and third place very close together until the Queen Elizabeth carriers are commissioned. After these navies I would place all the rest.

The Russians want their geopolitical role again, so they musts upgrade their Navy. And they seem to be doing something about it.

The Chinese will be the next great menace to the western "powers" (euphemism for USA + GB).

After USN it must be read:

2. Russian Navy
3. Chinese Navy

We are on the verge to see the colapse of the western hegemony because of their decay and lack to act upon the menaces that rise. On the other hand we have two very old and violent countries that want their place again. What do you think is going to happen? The USN would never risk 5,000+ lives on board of a CVN in order to really fight someone: Nimitz and Halsey days are long gone...

An appeaser is one who feeds a crocodile, hoping it will eat him last. Sir Winston Churchill

I don't know what will happen in the near future but today the Chinese don't deserve the third place. The navies of Japan and South Korea together with US technological assistance are better than the Chinese.

In that case I believe Quality over Quantity is the question my friends. The Chinese have enough patrol boats to sink Pearl Harbor ten times and still have enough to do circles around the old battlewagons. But the Aegis ships have the accuracy and range of a laser.

Never count the underdog out. Whoever does is in for a nasty surprise...

the Indian Navy should not be underestimated. They would absolutely slaughter the US Coast Guard, which has no significant anti surface military capability. They are a police force. The Indians have naval air, for one thing. If their professionalism is anything like what their air force displayed recently in an exercise with the USAF, they are very good indeed.

No one is to be underestimated never. That is the greatest sin in military art: underestimation and arrogance. You might see the ruskies or the chinese now with contempt but they are capable of great feats. The Indians already kicked once the pakistanies. Everybody must be taken with the same care and be cautious. And if you need to destroy them, it has to done as if they can fire nukes against your home...

An appeaser is one who feeds a crocodile, hoping it will eat him last. Sir Winston Churchill

There are several ways to measure modern military power, thus it is not an easy task to rank the world navies, however there are, arguably, two exceptions to this task when it comes to the 21st Century: (1) Forward Force Projection [FFP] and (2) the ability to use a nuclear weapon against one's foe(s) on the high seas.
This type of naval ability is often referred to as a "blue water navy." Because of the grand scope of the seas, FFP involves many considerations.
Briefly, a successfully assembled blue water Armada must be self efficient; have an air force greater in strength than all land/ sea based air power within striking distance; and carry within its' floatilla "seige weapons [SWP] like the American surface fleet's horde of cruise missiles.
In addittion, a naval power must have uncalcuable preparation, battle hardened training; and the ability to land a task force of soldiers(marines) on the ground at any moments' notice.
A powerful navy posesses an extremely high moral; a powerful modern navy maintains equipment and technology that are years ahead of all possible enemies. A great navy amaintains an Academy that consistently produces great military minds. A strong navy is backed by a free society of citizens and laws. A strong navy maintains a keen level of surprise and special forces.
A strong navy, most importantly, protects the Sea Routes of Free Trade and Commerce. A strong navy is capable of miraculous action at times of human suffering by offerring relief assistance.
Finally, a Strong Navy is a powerful navy.
The current, ten most power ful navies in the world are:
1. U.S. 4th Fleet.
2. U.S. 2nd Fleet
3. U.S. 7th Fleet
4. U.S. 3rd Fleet
5. U.S. 6th Fleet
6. U.S. 3rd Fleet
7. U.K. Royal Fleet
6. Japan
7. South Korea
8. Taiwan
9. India
10. Italy

I liked skipper´s analysis, indeed. The only comment (and it´s a comment, nothing more) is this:

A great navy amaintains an Academy that consistently produces great military minds. A strong navy is backed by a free society of citizens and laws.

Being a person that likes freedom above all I recon that freedom is not an indispensable requirement to produce an effective navy nor army nor air force. The military is a society into another society in which freedom is not the highest concept but that of honor, discipline, duty and self sacrificy. And none of these is a very "free" concept. As a matter of fact societies lacking any level of freedom had been able to produce good navies and outstanding officers. Of course, I do imagine that a soldier from a free society will find an extra purpose to fight in case of war. But that doesn´t mean that those under a tyranny will fight less.

Two cents, there.

An appeaser is one who feeds a crocodile, hoping it will eat him last. Sir Winston Churchill